Why use energy bar charts?

The usefulness of graphical representations over straight-up equations and calculations for understanding energy concepts has been well established in physics teaching literature for years.  Yet, still only a fraction of physics teachers - especially at the college level, as reported to me by recent graduates - use such representations as an integral part of teaching energy.  

For most teachers I work with, their story parallels my own.  At first, reluctance to use energy bar charts seems to have three possible causes:

(1) I was never taught that way; I and my classmates understood energy with equations without trouble.

(2) It would be a LOT of work to change my materials not just to add in bar charts, but to de-emphasize algebraic algorithms.  And it doesn't make sense to do this work because...

(3) My current students are understanding just fine; they're getting answers right more often than not.

I resisted teaching energy bar charts for nearly the first two decades of my career - mainly for point (3) above.  For the most part, my students seemed to be learning energy without trouble.  The old calculational AP Physics B exam rewarded quantitative reasoning.  So I taught my class the most general form of an energy conservation equation I could:

W_NC = (KE_B – KE_A) + (PE_B – PE_A)

Students were taught to identify two positions A and B, take out any terms that were zero, plug in the KE and PE formulas, and solve.  This allowed students to get correct answers, or at least copious partial credit, for practically any Physics B problem you could imagine.

This algebraic formulation caused difficulty when students were asked to reason with energy.  Most students dutifully plugged in correct variables, or correct numbers for the correct variables.  But what they *saw* was a bunch of gobbletygook, as if the work-energy theorem were written in Klingon.  

Yes, I'm personally fluent enough in mathematical notation that I can quickly describe conceptually how a change in a physical situation would affect the calculation.  Physics Education Research has provided abundant, replicable evidence that the vast majority of students are nowhere near as fluent.  

(Some would argue that students in a college-level physics class should be good enough at mathematics to do advanced analysis with an equation this simple; after all, most of these folks are in a calculus class, and algebra of this sub-basic level was generally taught in 7th or 8th grade!  Yet, arguing what students should be able to do in the face of evidence to the contrary is not a recipe for success.)

When the AP Physics 1 exam came on line in 2014-15, its incessant demands for non-quantitative reasoning forced my hand.  I opened up the wardrobe to find and create energy bar chart exercises, labs, problem sets, etc.  And lo, a new conceptual world opened up Narnia-style.

Look, would I have ever taught Newton's second law without free body diagrams?  Of course not!  If you just teach "F = ma," then students plug in any old F to the equation.  If you tell them they've used the wrong expression or number for F, they'll pull another out of their tuckus at random.  But the free body diagram forces* students to represent all the forces acting, and thus to pay attention to why each force might or might not exist, before they do any math at all.  The diagram ensures that students can't just plug numbers into equations in search of being done - they have to do the problem right.

* ha!

The purpose of an annotated energy bar chart is identical.  With just an equation to work from, students are trained from birth or middle school to plug in numbers and solve; exactly what numbers they use don't matter.  But now, students have no choice but to describe briefly why they chose to include or not include each bar representing a form of energy.  The exact size of the bars isn't important - just as I don't demand a to-scale free body diagram, I don't demand a to-scale energy bar chart.  What matters is whether there are more or fewer bars for each form of energy, or whether there are bars at all.

And finally, the energy bar chart gives students a starting point to get them out of their "I can't do this" inertia.  Anyone in my class, no matter how weak, can start drawing a free body diagram or an energy bar chart.  If they pay attention to their annotations, they often catch their own faulty reasoning.  When they seek help from me or a friend, the discussion begins with the diagram rather than with mathematics.  It's difficult for a student to understand why their mathematical work is wrong - especially when the actual mathematical algorithms were done correctly, but the starting assumptions were incorrect.  It's simple for a student to see why a diagram isn't right, and then to redo the mathematics based on the correct starting point.